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Re: triangles in circles
*To*: mathgroup at smc.vnet.net
*Subject*: [mg26856] Re: [mg26813] triangles in circles
*From*: Andrzej Kozlowski <andrzej at bekkoame.ne.jp>
*Date*: Thu, 25 Jan 2001 01:13:32 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
Here is some quickly written code that will create the points on the circle
and the triangles you want. I make use of the Combinatorica package to
construct all the choices of three points out of n.
First we load the package:
<< DiscreteMath`Combinatorica`
Next we get the coordinates of the points on the unit circle:
pts[n_] := {Re[#], Im[#]} & /@ Map[ExpToTrig, Table[E^(2Pi*I*k/n), {k, 1,
n}]]
Here are the triangles that can be made given n-points (n>2).
triangles[n_] :=
Line /@ KSubsets[pts[n], 3] /. Line[a_] :> Line[Append[a, First[a]]]
You can see them with:
Show[Graphics[{triangles[7]}], AspectRatio -> Automatic]
This can be improved in various ways, by adding the ciorcle, colour etc.
--
Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/
http://sigma.tuins.ac.jp/
on 1/24/01 6:18 PM, Tom De Vries at tdevries at shop.westworld.ca wrote:
> Hello all,
>
> I'm teaching a high school math class and we are doing permutations and
> combinations. One of the "standard" questions is ..."given a certain number
> of points located around a circle, how many triangles can be formed...."
>
> The simple line below creates a circle with 5 points arranged around it.
> Could someone help me with a way to generate the lists of points that would
> create all the triangles. I know that for more points it would get kind of
> messy, but I wanted to actually draw all the triangles as I thought it might
> be an interesting graphic...
>
> Thanks for any help you might have....
>
>
> n = 5;
>
> ptlist = Table[{Cos[i 2 \[Pi]/n], Sin[i 2 \[Pi]/n]}, {i, 1, n}];
>
> Show[Graphics[{
> Circle[{0, 0}, 1],
> {PointSize[0.02], Point /@ ptlist}
> }], AspectRatio -> Automatic]
>
> Sincerely, Tom De Vries
>
>
>
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